Geometrical device having articulated relatively movable sections



Aug. 24, 1965 R. D. RESCH 3,201,894

GEOMETRICAL DEVICE HAVING ARTICULATED RELATIVELY MOVABLE SECTIONS Filed J u 1963 INVENTOR Ronald D. Resch United States Patent GEQMETRECAL DEVliClE HAVENG ARTICULATED RELATIVELY MUVABLE dECTlGNS Ronald D. Beach, 1000 E. 24 Highway, Independence, Mo. Filed June 14, 1%3, Ser. No. 237,967 8 Claims. (61. 46-1) device can be constructed from a plurality of polygons interconnected at the corners of the polygons into mod ular arrangement. The sections are pivotally interconnected in a novel pattern so that the module, in an initial closed position with each section abutting an adjacent section, may be moved to an expanded position with spacing between the respective sections by rotating one section in a first direction. Such rotation of the one section moves every other section of the module in a different direction. Reversing the direction of rotation of the section causes the module to return to its closed position.

One feature of the novel arrangement of sections and connectors of the device of this invention is that the size of the device may be increased by merely adding additional sections to the module. A device may be comprised of as many sections as desired so long as the pattern of, interconnecting the sections is continued with the added sections.

' The novel pattern of interconnection of the sections which results in relative movement of each section of a single module in different directions when one section is rotated to thereby cause expansion or contraction of the module contributes appreciably to the wide variety of uses which may be made of the device. Accordingly, it is the most important object of this invention to provide a device comprising a plurality of geometric sections interconnected in a novel manner into modular arrangement whereby rotary movement of one of the sections of a module results in individual movement of each of the other sections of the module in different directions.

Another important object of the invention is to provide a device wherein all of the sections may be initially arranged in a compact grouping but which may be shifted as a result of the novel arrangement of the sections by movement of one of the sections to an expanded arrangement providing spacing between the respective sections.

Still a further object of the invention is to provide a device which may be moved to the open arrangement of its sections and back to the closed arrangement thereof by the simpie expedient of rotation of one of the sections first'in one direction and then in the other direction.

A yetfurther objector the invention is to provide a device which is capable of a wide' variety of uses by virtue of its capability of being shifted readily in a predetermined geometric pattern from its closed arrangement covering a relatively small area to its open arrangement covering a relativelylarge area.

Still other important objects of this invention will be pointed out or will become more apparent as the specification progresses.

In the drawing:

FIGURE I is a plan view of one form of the device embodying the principles of this invention. showing the device in its closed arrangement; v

FIG. 2 is a plan view of the device of KG. 1 showing the arrangement of the sections in an intermediate position between the closed and open arrangementof the device; p t

a plan view of the device of FIG. 1 showing FIG. 3 is ag ast Patented Aug. 24, 1965 the arrangement of the sections with the device in its fully open position;

FIG. 4 is a plan view of another form of the device embodying the principles of the invention showing the arrangement of the sections thereof in the fully closed position of the device:

FIG. 5 is a plan view of the device of FIG. 4 showing the arrangement of the sections in a partially open position of the device;

FIG. 6 is a plan view of still another device embodying the principles of this invention showing the arrangement of the sections when the device is in its fully closed position;

FIG. 7 is a plan view of the device of FIG. 6 showing the arrangement of the sections when thedevice is in a partially open position; and

FIG. 8 is a fragmentary, perspective view of another device embodying the principles or" this invention wherein the sections are prisms.

Referring initially to FiGURE 1, the device embodying the principles of this invention is broadly denoted by the numeral 10 and comprises a plurality of geometric sections which, in this form of the device 10, are squares. There is a centrally disposed section 12 circumscribed by a plurality of sections having side margins equal to the margins of section 12 and numerated 14, 16, 18, 20, 22, 24, 26 and 28. The sections 12-23 comprise one module of the device 10 and it will be noted that the sections 16, 2t 24 and 28 are positioned with one side margin of each section lying in substantial abutting disposition with respect to a corresponding side margin of the central section 12.

The abutting side margins of sections 16, 20, 24 and 28 are in coextensive alignment with the respective side margins of central section 12. Section 18 is positioned between sections 16 and 2t and has a pair of its adjacent side margins positioned coextensively with and in substantial abutting disposition with respect to the proximal margins of sections 16 and 20. Similarly, the sections 22, 26 and 14 are positioned between the sections 20 and 24, 24 and 28, and 28 and 16 respectively, as shown in FIG. 1. Thus, it is apparent that each of the outer sections 14 28 are positioned with two side margins of each section in substantial abutting disposition with respect to two imaginary straight lines lying along any two adjacent side margins of the central section 12 when the module is in the closed position illustrated in FIG. 1.

Device 10 is shown in FIGS. 1, 2 and 3 as comprising but a single module which includes a central section 12 and a ring of outer sections 14-28 disposed in continuous circumscribing disposition with respect to central section 12. It will be readily understood, however, that device 10 could include more sections interconnected with the adjacent sections. It is deemed suflicient, however, to explain the principles of this invention to show device 10 comprised of but one module.

The sections of the module of device 10 are interconnected by pivot structures or hinge means 3th which may take any form. It is sufiicient that particular corners of the section be pivotally interconnected with proximal corners of adjacent sections so that one section is free to rotate at its corner about the point of connection with the adjacent section. The hinges 30 chosen for illustration comprise elongated strips of flexible material having opposed end margins thereof firmly secured by adhesive or the like to the sections interconnected by the hinges. By referring to FIGS. 1, 2 and 3 of the drawing, it is clearly apparent that there is a hinge 3t) pivotally interconnecting each corner of the central section 12 with a'corner of the outer sections 28, 16, 20, and 24. There is also provided a hinge 30 connecting a pair of the corners of the sections 14, 18, 22 and 26 with the proximal "corners egor-e974}- 1 it is possible to move feach se'ction'of' the modulejina I ditf erent-direction and to expand'the module'fror'nthe.

closed position thereof by sirnply rotating a single 1 section of thernodule.- I Forexa'mple, iffse'ction l2 r tated in a clockwise direction as'Ni'ewed in FIG; 2, the

other sections of the module'are ,causedto both rowel,

and translate to provide spacing between the sections; Such clockwise rotation offsection 12 fcauses v. section 16 I to rotate in a counterclockwise directionandfalso to Wise direction but translates inrai direction at right angles" frornthe direction of translation:of jsection 16 and in the direction indicated b'ythe arrow proximal 'sec tionlfl" c ..r r v 115' translate in a direction indicated by: the arrow.- at .the top of FIG. 2. SectionZO also rotates in 'accountercloek-f I section J ,pivotally, interconnected by hinges 62 with theproximall corners of adjacent sections as'illustrated; Thus,,section 38,-in addition to being pivotally;

interconnected at one, corner to section 36, is pivotally ninter'connected at the; other corner s to the proximal corners of respective sections'44 and GO-as shown. Likewise, section ;is pivotally interconnected to section '36 at qne corner and at the" other. corners to the proximal corners of 's ectionsi48 and' SO as shown. In .the same mannensection' iz is;pivotally interconnected at one 7 :corner to 'sectionfid-and at eachlof the other corners to' the correspondingproximal corners of respective secj tions54{and 56 .as'lshown." fAdditionally, section 58 is "pivotallyiinterconnected at -a pair offcorners thereo'ftoi corners of sections 56;and' 60, -while-sect'ion 46 is pivotally interconnected to' sections and 48, and section 52 is pivot'allyinterconnectedto sections 50 and :54, all as 7 "shown clearly-in FIGS. -4- andlSf It will be noted that device 34faschereinab oveset forth with respect to at the right of FIG. 2, Ina similar manner/section 231 beside section 28 at the left of FIG; 2. f

Simultaneously, the clockwise rotation of section 12 V is caused to rotate -in'a counterclockwisedirection but; inthe direction indicated by -the arrow at'the' bottornfof 516.2, while section 23,-also rotating in acouhterclock: wise direction, translates inthe direction ofji th'e' arrow device 10, argiven corneriofeachzof thesections of the rnodule is'connectedto but a single corner of anadjacent section." 3 1 The section's 'of the module can-eachbecaused to move T i-hra differentdirection by simply rotating a single section fjof the modulei Thusfif'central sectioned is causedto rotate I in '3' clockwise direction; the other interconnected sectionsfof the module are each caused to rotate toward causes clockwise rotation ofsections 18,"2 2;'2 6 and 1 4 u 7 i V V H V i L section is causedto translate'generallyalong linesvp'assing and translational "movement of the s ectionsj on' diagonal" lines radiating 'outwardly from the axis" of rotation- 10i,

section lz and passing through therespective sections 1s,"22,,2 6 and14. V I ,7

An inspection of FIG. ,2, revealsthat this" movement ofthe' sections produces'spa'cings 32 between the: central":

section 12' and the outer sections 14'28.v There are of'section 12 through an arc'of causes the arrange the individual sections .of the 'device'lof It-willbe readily understood that I rotation of secti'o "12 through an'equal arc in a counterclockwise idirtiofiwill {result .7

a in 'theshiftingof the individual sections of the module, v e

back into the initial position shown in FIGQI "whereinc the side margins ofthe sections are; in closeabutting re; lationship with, the 'side "margins" of adja'centisectionsl;' Y The area covered by device 10 in theopen-position there-Q I of illustratedin FIG S, is vastly greater than areal fo'f the device 10 sholwnin it s closed'position "inEIG."-1 r" Anotheriform of the inventionis illustrated; in EIGS tratedinFIG.'4. it ,7 e Similarly, there are) provided sections? 5 Pit al y n e nectin each ;,t Qf Ts ntt'a i se 4 s hown rlyi F G Additionallygapairiofthe'othe eiirs'o eac 35 four cspacingsgfizfor each module. Continued-rotation, I

spacings 32 cover a maximum area and are *as largeias 40= i V vention comprise s a deviceo66 sirnilar'v to device 10 where "posit-ions shown ll'l FIGISQ 'In addition torotation, each through the: axis -of r otation ofth e rotati'n'g central rnem 'ber 36 and entending'through the corresponding sections. Such inovementoflthe'f sectionsrcausesfspacings d i between the centrallsectionf 2:6"a'nd the outer sections' 38-6t) as shown in'FIG'. 5; r Continued rotation of centraln 'section' 36lcauses enlar gc-rrnerrt of thejs'pacings 64 a s will-be readily understood; Likewiserotation' of section 36 in. the opposite direction; frornjthat'iliustrated by the arrow in FIG, 5 causesthereturn of {the sections of the module. fro-the" closed position'rthereoffas shown in FIG.;5; It

7 carr be appreciate dthat device 34 occupies considerably :larger area in its open position than inthejclosed position Referring n WtoFIQSgdernd 7; the form of the inin the sectionsfarerhomboidal. The arrangement of the ,sse ction's' is identical to that. set forth in 'de'tailiwith respect to 'devi'cellfl and will be'omitted fonthe sake of brevity.

' It shouldlbe pointed-out; however, that the corners of between sections 40 a'nd 42 and; sec'ti ons 56 5,8.andr6Qf w ia stiq sj and 385 3 show l 7 'It will th bes'een thatfsections slis tl n r continuous,;circurnscribing,. 'pr'oxinrali-reiatlonship to 1 p meter? seatml Gland 68 mu the sectionsare' interconnectedin. armanner corresponding withj device .1 0fa11d byfpivot Structures or hinges 68 V which 'rnaybe 'identicalto pivot structures or hinges '30, i. The rngdule 0t idevice 566 'includes' a central section 70 anda plurality;of circumscribing sections /72, 74', ,76,'

7 ;";1'812', 841 nd; 86. Viewing ran, it; will b seen as set forthwith "respect: to device 10 "Such {movement is a diiferentdirection I and resultsfinl spacings-88 etween thelsections, Rotation of ceintr'ail-"sectionfiOflintlieQ po sit'e jdirection'causes thernod ule}to returnoits position asshowir in V iFIGQLG: Obviously, device 7 66;;occupie's a relatively larger 1 ar ea in'its open'position'than in the'closjed position there-v y The[particular construction'gofthe 62 and -'68'fo rr nzno'part.o f theinventio perf se;itbeingsufllcient that athey are' i flexible to per it? pivotal interconnecting 1i1t 'theijlullyclosed posi- ,7 r V ic i n lying n" butting dis position:yvift respect the proxi-; c

f adjacent: sections; TTIieQhinges :30, a wise. be flexible to permit shifting of the sections to the closed positions of the respective devices 10, 34 and 66 as herein previously explained.

. The devices chosen for illustration have included squares and rhombodial sections, as well as triangular sections. However, sections which are parallelograms of any specific shape are suitable for constructing devices according to the principles of this invention.

It is contemplated by this invention that the sections of the devices 10, 34 and 66 could be constructed from relatively flat sheet material. Thus, the description to this point has been directed toward sections comprised of squares, triangles, and rhombuses. However, the invention could be equally advantageously carried out if thesections were constructed from blocks of material having a substantial third dimension. Thus, device could be constructed from prisms, it being suificient that one side thereof is square. Likewise devices 34 and 66 could also be constructed from prisms having one side thereof triangular and rhomboidal respectively.

The device 90, fragmentarily illustrated in FIG. 8, includes a plurality of sections 92 which comprise prisms interconnected along their corners by elongated strips 94 of flexible material. The device 90 is shown in its fully open position to present spacings 96 between the respective sections 92.

The devices constructed according to the principles of this invention are quite versatile. For example, it has been found that devices constructed with one or more modules of articulated sections is particularly well adapted as a toy wherein a single section may be grasped to permit expansion or contraction of the device by simply manually rotating one of the sections. The sections may be colored in a variety of ways to impart attractiveness to the object. It is contemplated that the individual sections of the devices could be molded from plastic material or the like and that they could take the form of open-top vessels into which might be placed objects such as childrens blocks or the like. The blocks could be readily removed and replaced with other blocks which might be of diiferent colors so that the child could change the geometric pattern formed by the sections of the devices.

Further, it has been found that the novel construction of devices in the manner contemplated by this invention results in a device which is particularly well adapted for use as a mat to be placed in protective disposition over a planar surface. For example, devices constructed in this manner are well suited for use by housewives or the like in placing under hot dishes, kettles or the like for protecting tables and other surfaces. When it is desired to use the device with a relatively small vessel, the device may be employed in its closed position. If, however, it is necessary to protect the surface from a much larger vessel, the device may be readily moved to the expanded position thereof wherein an appreciably greater surface is thereby protected.

Still other very important uses which have been found for devicesof this construction include the presentation of animated signs. One such use contemplates the presentation of certain information on an exposed face of the sections when the device is in its closed position. Movement'of the device to its open position may result in obliteration of the information first displayed and the exposure of other information which was not observable when the device was in its closed position. This may be 'achieved by Virtue of having information appearing at the spacings 32, 64, 88 or 96 which could not be seen until the device reached its open position. The result could also be achieved by the use of special light-reflective surfaces whereby the shifting of the sections from one position to the other disposes the surfaces with respect to the observer in such a manner that information on the sections observable at one position thereof could not be discerned at another position, whereas different information would thereupon be displayed. A variety of means could be utilized for motivating the shifting of the device from the closed to the open position and the return to the closed position. Such motivation is enhanced and appreciably simplified by virtue of the fact that it is merely necessary to motivate but one of the sections to achieve resultant motivation of all of the rest of the sections in the manner hereinabove set forth.

It should be stressed that although a single module has been shown for each device for illustrative purposes, the devices may comprise many modules interconnected in the pattern hereinabove set forth. Additionally, each module might have a single row of sections therearound or even a few sections attached to the outer sections of the module. If the pattern of interconnection which has heretofore been set forth and is clearly illustrated in the drawing is followed, the other additional sections of the device will operate in a similar manner to those described.

Having thus described the invention, what is claimed as new and desired to be secured by Letters Patent is:

1. A geometric device comprising:

a plurality of relatively shiftable, polygonal sections in modular arrangement to define a module and including a central section and a plurality of outer sections, said outer sections being disposed in continuous circumscribing, proximal relationship to the perimeter of said central section, each of said outer sections having side margins thereof positioned in coextensive, substantially abutting relationship with the side margin of an adjacent outer section, a side edge of an outer section adjacent to said central section being disposed in proximal coextensive, substantially abutting disposition With respect to an adjacent side of said central section when the module is in a closed condition;

means pivotally interconnecting each corner of the central section with the proximal corner of the outer section adjacent thereto; and

means pivotally connecting a pair of the other corners of each outer section with the proximal corners of the outer sections adjacent thereto to permit movement of all of the sections when said central section is rotated, a corner of each section being interconnected with but a single corner of another section of the module.

2. A device as set forth in claim 1 wherein said sections are parallelograrns.

3. A device as set forth in claim 1, wherein said sections are square.

4. A device as set forth in claim 1, wherein said sections are triangular.

5'. A device as set forth in claim 1, wherein said sections are rhomboidal.

6. A geometric device comprising:

a plurality of relatively sh'iftable square sections in modular arrangement to definea module and includ ing a central section and a plurality of outer sections, said outer sections being disposed in continuous, circumscribing, proximal relationship to the perimeter of said central section, said outer sections being positioned with two side margins of each outer section in substantial abutting disposition with respect to two imaginary straight lines lying along two adjacent side margins of the central section when the module is in a closed position; and

means pivotally interconnecting the sections of the module, said means including first structure interconnecting the corners of said central section to the proximal corners of respective, adjacent outer sections and second structure interconnecting a corner of each of said respective, adjacent outer sections adjacent to its said proximal corner to the proximal corner of the outer section adjacent thereto, a corner of each section being interconnected with but a single corner of another section, whereby the sect-ions may 

1. A GEOMETRIC DEVICE COMPRISING: A PLURALITY OF RELATIVELY SHIFTABLE, POLYGONAL SECTIONS IN MODULAR ARRANGEMENT TO DEFINE A MODULE AND INCLUDING A CENTRAL SECTION AND A PLURALITY OF OUTER SECTIONS, SAID OUTE SECTIONS BEING DISPOSED IN CONTINUOUS CIRCUMSCRIBING, PROXIMAL RELATIONSHIP TO THE PERIMETER OF SAID CENTRAL SECTION, EACH OF SAID OUTER SECTIONS HAVING SIDE MARGINS THEREOF POSITIONED IN COEXTENSIVE, SUBSTANTIALLY ABUTTING RELATIONSHIP WITH THE SIDE MARGIN OF AN ADJACENT OUTER SECTION, A SIDE EDGE OF AN OUTER SECTION ADJACENT TO SAID CENTRAL SECTION BEING DISPOSED IN PROXIMAL COEXTENSIVE, SUBSTANTIALLY ABUTTING DISPOSITION WITH RESPECT TO AN ADJACENT SIDE OF SAID CENTRAL SECTION WHEN THE MODULE IS IN A CLOSED CONDITION; MEANS PIVOTALLY INTERCONNECTING EACH CORNER OF THE CENTRAL SECTION WITH THE PROXIMAL CORNER OF THE OUTER SECTION ADJACENT THERETO; AND MEANS PIVOTALLY CONNECTING A PAIR OF THE OTHER CORNERS OF EACH OUTER SECTION WITH THE PROXIMAL CORNERS OF THE OUTER SECTIONS ADJACENT THERETO TO PERMIT MOVEMENT OF ALL OF THE SECTIONS WHEN SAID CENTRAL SECTION IS ROTATED, A CORNER OF EACH SECTION BEING INTERCONNECTED WITH BUT A SINGLE CORNER OF ANOTHER SECTION OF THE MODULE. 